Multiplication table

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In mathematics, a multiplication table (sometimes, less formally, a times table) is a mathematical table used to define a multiplication operation for an algebraic system.

The decimal multiplication table was traditionally taught as an essential part of elementary arithmetic around the world, as it lays the foundation for arithmetic operations with our base-ten numbers. Many educators believe it is necessary to memorize the table up to 9 × 9. In countries using the Imperial system of measurement, such as the United States, it is often considered helpful to memorize the table up to 12 × 12.

The times tables were invented by the Chinese.[citation needed]

× 1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20
1 1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20
2 2 4 6 8 10 12 14 16 18 20 22 24 26 28 30 32 34 36 38 40
3 3 6 9 12 15 18 21 24 27 30 33 36 39 42 45 48 51 54 57 60
4 4 8 12 16 20 24 28 32 36 40 44 48 52 56 60 64 68 72 76 80
5 5 10 15 20 25 30 35 40 45 50 55 60 65 70 75 80 85 90 95 100
6 6 12 18 24 30 36 42 48 54 60 66 72 78 84 90 96 102 108 114 120
7 7 14 21 28 35 42 49 56 63 70 77 84 91 98 105 112 119 126 133 140
8 8 16 24 32 40 48 56 64 72 80 88 96 104 112 120 128 136 144 152 160
9 9 18 27 36 45 54 63 72 81 90 99 108 117 126 135 144 153 162 171 180
10 10 20 30 40 50 60 70 80 90 100 110 120 130 140 150 160 170 180 190 200
11 11 22 33 44 55 66 77 88 99 110 121 132 143 154 165 176 187 198 209 220
12 12 24 36 48 60 72 84 96 108 120 132 144 156 168 180 192 204 216 228 240
13 13 26 39 52 65 78 91 104 117 130 143 156 169 182 195 208 221 234 247 260
14 14 28 42 56 70 84 98 112 126 140 154 168 182 196 210 224 238 252 266 280
15 15 30 45 60 75 90 105 120 135 150 165 180 195 210 225 240 255 270 285 300
16 16 32 48 64 80 96 112 128 144 160 176 192 208 224 240 256 272 288 304 320
17 17 34 51 68 85 102 119 136 153 170 187 204 221 238 255 272 289 306 323 340
18 18 36 54 72 90 108 126 144 162 180 198 216 234 252 270 288 306 324 342 360
19 19 38 57 76 95 114 133 152 171 190 209 228 247 266 285 304 323 342 361 380
20 20 40 60 80 100 120 140 160 180 200 220 240 260 280 300 320 340 360 380 400

Contents

[edit] Traditional use

In 493 A.D., Victorius of Aquitaine wrote a 98-column multiplication table which gave (in Roman numerals) the product of every number from 2 to 50 times and the rows were "a list of numbers starting with one thousand, descending by hundreds to one hundred, then descending by tens to ten, then by ones to one, and then the fractions down to 1/144" (Maher & Makowski 2001, p.383)

The traditional rote learning of multiplication was based on memorization of columns in the table, in a form like

  1 × 10 = 10
  2 × 10 = 20
  3 × 10 = 30
  4 × 10 = 40
  5 × 10 = 50
  6 × 10 = 60
  7 × 10 = 70
  8 × 10 = 80
  9 × 10 = 90

 10 x 10 = 100
 11 x 10 = 110
 12 x 10 = 120
 13 x 10 = 130
 14 x 10 = 140
 15 x 10 = 150
 16 x 10 = 160
 17 x 10 = 170
 18 x 10 = 180
 19 x 10 = 190
 100 x 10 = 1000

This form of writing the multiplication table in columns with complete number sentences is still used in some countries instead of the modern grid above.

[edit] Patterns in the tables

There is a pattern in the Multiplication table which is useful for the children to memorize the tables.

Look at the figure below

    →                 →
  1 2 3             2   4
↑ 4 5 6 ↓         ↑       ↓
  7 8 9             6   8
    ←                 ←
    0                 0
  Fig-1             Fig-2

For example, to memorize all the multiples of 7

  1. Look at 7 in the above picture and follow arrow.
  2. Next number in the arrow is 4. So think of the next immediate number end with 4 after 7 that is 14.
  3. Next number in the arrow is 1. So think of the next immediate number end with 1 after 14 that is 21.
  4. Once the row is over start with next row in the same direction. The number is 8. So think of the next immediate number ends with 8 after 21. it is 28.
  5. Proceed in the same way till the last number 3 it corresponds to 63
  6. Next include 0 at the bottom. it corresponds to 70
  7. Then start with 7 this time it will corresponds to 77
  8. And it continues.

Fig-1 is used for multiples of 1,3,7,9 and Fig-2 is used for the multiples of 2,4,6,8.

Using this pattern you can memorize the multiples of any number 1 to 9 except 5.

[edit] In abstract algebra

Multiplication tables can also define binary operations on groups, fields, rings, and other algebraic systems. In such contexts they can be called Cayley tables. For an example, see octonion.

[edit] Standards-based mathematics reform in the USA

In 1989, the National Council of Teachers of Mathematics (NCTM) developed new standards which were based on the belief that all students should learn higher-order thinking skills, and which recommended reduced emphasis on the teaching of traditional methods that relied on rote memorization, such as multiplication tables. Widely adopted texts such as Investigations in Numbers, Data, and Space (widely known as TERC after its producer, Technical Education Research Centers) omitted aids such as multiplication tables in early editions. It is thought by many[who?] that electronic calculators have made it unnecessary or counter-productive to invest time in memorizing the multiplication table. NCTM made it clear in their 2006 Focal Points that basic mathematics facts must be learned, though there is no consensus on whether rote memorization is the best method.

[edit] See also

[edit] External links

Retrieved from "http://en.wikipedia.org/wiki/Multiplication_table"